It is interesting to note that topology can affect the amplitude
of CMB fluctuations on large angular scales.
Thus Ref. [1]} showed that
dodecahedral space topology in a spatially flat universe
can suppress the amplitude
of CMB fluctuations on the largest angular scales,
thus explaining some of the large scale CMB anomalies.
Similar results were found
in Ref. [2]},
where the authors used
\({R}^2\times S^1\)  topology
to explain the deficit in low CMB multipoles. These findings are to be contrasted with
the Planck 2013 [3]}, where one reads:
“we consider flat spaces with cubic toroidal (T3), equal-sided chimney
(T2) and slab (T1) topologies, three multi-connected spaces of constant positive curvature (dodecahedral, truncated cube and octahedral) and
two compact negative-curvature spaces. These searches yield no detection of the compact topology with the scale below the diameter of the last
scattering surface.”
